Stable ergodicity of skew products

Keith Burns; Amie Wilkinson

Annales scientifiques de l'École Normale Supérieure (1999)

  • Volume: 32, Issue: 6, page 859-889
  • ISSN: 0012-9593

How to cite

top

Burns, Keith, and Wilkinson, Amie. "Stable ergodicity of skew products." Annales scientifiques de l'École Normale Supérieure 32.6 (1999): 859-889. <http://eudml.org/doc/82505>.

@article{Burns1999,
author = {Burns, Keith, Wilkinson, Amie},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {stable ergodicity; inframanifold; skew products},
language = {eng},
number = {6},
pages = {859-889},
publisher = {Elsevier},
title = {Stable ergodicity of skew products},
url = {http://eudml.org/doc/82505},
volume = {32},
year = {1999},
}

TY - JOUR
AU - Burns, Keith
AU - Wilkinson, Amie
TI - Stable ergodicity of skew products
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1999
PB - Elsevier
VL - 32
IS - 6
SP - 859
EP - 889
LA - eng
KW - stable ergodicity; inframanifold; skew products
UR - http://eudml.org/doc/82505
ER -

References

top
  1. [AKS] R. ADLER, B. KITCHENS and M. SHUB, Stably ergodic skew products, Discrete and Continuous Dynamical Systems, Vol. 2, 1996, pp. 349-350. Zbl0989.37019MR97d:58113
  2. [B1] M. BRIN, Topological transitivity of one class of dynamical systems and flows of frames on manifolds of negative curvature, Func. Anal. Appl., Vol. 9, 1975, no. 1, pp. 9-19. Zbl0357.58011MR51 #6886
  3. [B2] M. BRIN, The topology of group extensions of C systems, Mat. Zametki, Vol. 18, 1975, no. 3, pp. 453-465. Zbl0332.58010MR52 #15563
  4. [BP] M. BRIN and Ja. PESIN, Partially hyperbolic dynamical systems, Math. USSR Izvestija, Vol. 8, 1974, no. 1, pp. 177-218. Zbl0309.58017
  5. [BPW] K. BURNS, C. PUGH and A. WILKINSON, Stable ergodicity and Anosov flows, to appear in Topology. Zbl0930.37008
  6. [CE] J. CHEEGER and D. EBIN, Comparison Theorems in Riemannian Geometry, North Holland/American Elsevier, 1975. Zbl0309.53035MR56 #16538
  7. [FP] M. FIELD and W. PARRY, Stable ergodicity of skew extensions by compact Lie groups, Topology, Vol. 38, 1999, No 1, pp. 167-187. Zbl0924.58045MR2000h:37038
  8. [GPS] M. GRAYSON, C. PUGH and M. SHUB, Stably ergodic diffeomorphisms, Ann. Math., Vol. 140, 1994, pp. 295-329. Zbl0824.58032MR95g:58128
  9. [H] S. HELGASON, Differential Geometry, Lie Groups, and Symmetric Spaces, Academic Press, 1978. Zbl0451.53038MR80k:53081
  10. [HPS] M. HIRSCH, C. PUGH and M. SHUB, Invariant Manifolds, Lecture Notes in Mathematics, Vol. 583, Springer-Verlag, 1977. Zbl0355.58009MR58 #18595
  11. [Hu] S.-T. HU, Homotopy Theory, Academic Press, 1959. Zbl0088.38803MR21 #5186
  12. [Hum] J. HUMPHREYS, Introduction to Lie Algebras and Representation Theory, Springer Verlag, 1972. Zbl0254.17004MR48 #2197
  13. [J] J.-L. JOURNÉ, A regularity lemma for functions of several variables, Rev. Mat. Iberoamericana, Vol. 4, 1988, no. 2, pp. 187-193. Zbl0699.58008MR91j:58123
  14. [KK] A. KATOK and A. KONONENKO, Cocycles' stability for partially hyperbolic systems, Math. Res. Lett., Vol. 3, 1996, no. 2, pp. 191-210. Zbl0853.58082MR97d:58152
  15. [Ma1] A. MANNING, There are no new Anosov diffeomorphisms on tori, Amer. J. Math., Vol. 96, 1974, pp. 422-429. Zbl0242.58003MR50 #11324
  16. [Ma2] A. MANNING, Anosov diffeomorphisms on nilmanifolds, Proc. Amer. Math. Soc., Vol. 38, 1973, pp. 423-426. Zbl0242.58004MR49 #8059
  17. [Mi] J. MILNOR, Morse Theory, Princeton University Press, 1969. 
  18. [N] K. NOMIZU, Lie Groups and Differential Geometry, Mathematical Society of Japan, 1956. Zbl0071.15402MR18,821d
  19. [P] W. PARRY, Entropy and Generators in Ergodic Theory, W. A. Benjamin, Inc. 1969. Zbl0175.34001MR41 #7071
  20. [PP] W. PARRY and M. POLLICOTT, Stability of mixing for toral extensions of hyperbolic systems, Tr. Mat. Inst. Steklova, Vol. 216, 1997, Din. Sist. i Smezhnye Vopr., pp. 354-363. Zbl0988.37034MR99g:58094
  21. [PS1] C. PUGH and M. SHUB, Stably ergodic dynamical systems and partial hyperbolicity, J. of Complexity, Vol. 13, 1997, pp. 125-179. Zbl0883.58025MR98e:58110
  22. [PS2] C. PUGH and M. SHUB, Stable ergodicity and julienne quasiconformality, September, 1997 preprint. 
  23. [R] D. RUDOLPH, Classifying the isometric extensions of a Bernoulli shift, J. Analyse Math., Vol. 34, 1978, pp. 36-60. Zbl0415.28012MR80g:28020
  24. [Wa] C. WALKDEN, Stable ergodic properties of cocycles over hyperbolic attractors, 1997 preprint. 
  25. [Wi] A. WILKINSON, Stable ergodicity of the time one map of a geodesic flow, Ergod. Th. and Dynam. Syst., Vol. 18, 1998, no. 6, pp. 1545-1588. Zbl0915.58079MR99m:58129
  26. [Y] H. YAMABE, On an arcwise connected subgroup of a Lie group, Osaka Math. J., Vol. 2, 1950, pp. 13-14. Zbl0039.02101MR12,158a

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.